Stabilization of Migration Deconvolution Jianxing Hu University of Utah

Outline MotivationMotivation MethodologyMethodology Numerical TestsNumerical Tests ConclusionsConclusions

KMMD Time (s) X(km) Time (s) X(km)

Comparison of RTM and MD Images 6 X(km) X(km) Depth (km) Depth (km) 1 6 X(km) X(km) Depth (km) Depth (km) RTMMD

Motivation Investigate banding noise in the MD image and improve the stability of MD system. Banding X(km) Depth(km)

Outline MotivationMotivation MethodologyMethodology Numerical TestsNumerical Tests ConclusionsConclusions

Migration Noise Problems AliasingAliasing Recording FootprintRecording Footprint Limited ResolutionLimited Resolution Amplitude DistortionAmplitude Distortion 0 km 0 km 15 km 15 km Migration noise and artifacts Footprint Amplitude distortion 0 2 Time (s)

Solution: Deconvolve the point scatterer response from the migrated image T r = (L L ) m Reflectivity Migrated Section Section Reason: m = L d TMigratedSectionData but d = L r L r Migration Section = Blured Image of r = L L Define T as migration Green’s function

Depth Slices of Point Scatterers Kirch. Migration Image Kirch. Migration Image MD Image MD Image 0 X(km) X(km) 1 Y(km) Y(km) X(km) X(km) 1 Y(km) Y(km) 0 1 m = L L r m = L L rT r = (L L ) m T -1

Migration Deconvolution Model Space Model Space --- reference position of migration Green’s function

MD System of Equations where represents the spectrum of on the depth of with a scatterer located at

Migration Green’s Function Coefficient Matrix Structure Diagonal element Off-diagonal element Coefficient matrix regularization

Artifacts in MD Poststack Poststack MD Image MD Image 0 4 X (km) X (km) Depth (km) Depth (km) 0 Banding Noise Coefficient Matrix Condition Number v.s. Wavenumber Wavenumber (radian/m)

Stabilization of MD System Equations Monitor the condition number of MD system equation for each wavenumber Monitor the condition number of MD system equation for each wavenumber If wavenumber <preset tolerance Otherwise

Outline MotivationMotivation MethodologyMethodology Numerical TestsNumerical Tests ConclusionsConclusions

Numerical Tests 2-D SEG/EAGE overthrust model poststack MD2-D SEG/EAGE overthrust model poststack MD 3-D SEG/EAGE salt model poststack MD3-D SEG/EAGE salt model poststack MD 2-D SEG/EAGE overthrust model prestack MD2-D SEG/EAGE overthrust model prestack MD

Regularization of MD System Equations Poststack Poststack MD Image MD Image without without regularization regularization 0 4 X (km) X (km) Depth (km) Depth (km) X (km) X (km) Depth (km) Depth (km) 0 Poststack Poststack MD Image MD Image with with regularization regularization

Numerical Tests 2-D SEG/EAGE Overthrust Model Poststack MD2-D SEG/EAGE Overthrust Model Poststack MD 3-D SEG/EAGE Salt Model Poststack MD3-D SEG/EAGE Salt Model Poststack MD 2-D SEG/EAGE Overthrust Model Prestack MD2-D SEG/EAGE Overthrust Model Prestack MD

Kirchhoff Migration Images X (km) Depth (km) Inline Section Y (km) Depth (km) Crossline Section

MD Images no Regularization X (km) Depth (km) Inline Section Y (km) Depth (km) Crossline Section

MD Images with Regularization X (km) Depth (km) Inline Section Y (km) Depth (km) Crossline Section

Comparison of Migration and MD Image X (km) Depth (km) Migration Inline Section X (km) Depth (km) MD inline Section

Comparison of Migration and MD Image Y (km) Depth (km) Migration Crossline Section Y (km) Depth (km) MD Crossline Section

KM Inline (97,Y) Section MD Inline (97,Y) Section 58 Y (km) Depth (km)

KM Crossline (X,97) Section MD Crossline (X,97) Section 04 2 Depth (km) 118 X (km) 118 X (km) 04 2

Numerical Tests 2-D SEG/EAGE Overthrust Model Poststack MD2-D SEG/EAGE Overthrust Model Poststack MD 3-D SEG/EAGE Salt Model Poststack MD3-D SEG/EAGE Salt Model Poststack MD 2-D SEG/EAGE Overthrust Model Prestack MD in COG2-D SEG/EAGE Overthrust Model Prestack MD in COG

Regularization of MD System Equations Prestack Prestack COG COG Migration Migration Image Image m m without without regularization regularization 0 4 X (km) X (km) Depth (km) Depth (km) X (km) X (km) Depth (km) Depth (km) 0 Prestack Prestack COG COG Migration Migration Image Image m m with with regularization regularization

Conclusions Worse condition number causes the banding noise in MD results Condition number is related to the wavelet frequency, position of migration Green’s function and velocity medium Regularization of the MD system equations enhances the stability of MD system

Acknowledgement Thanks to 2000 UTAM sponsors for their financial supportThanks to 2000 UTAM sponsors for their financial support Thanks to Advanced Data Solutions for providing the SEG salt model migration resultThanks to Advanced Data Solutions for providing the SEG salt model migration result

Motivation Investigate Banding Noise in the MD image and improve the stability of MD system.